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Choice probability generating functions

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  • Fosgerau, Mogens
  • McFadden, Daniel
  • Bierlaire, Michel

Abstract

This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with specific properties, and that every function with these specific properties is consistent with a RUM. The choice probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized by logarithmic mixtures of their associated CPGF. The paper relates CPGF to multivariate extreme value distributions, and reviews and extends methods for constructing generating functions for applications. The choice probabilities of any ARUM may be approximated by a cross-nested logit model. The results for ARUM are extended to competing risk survival models.

Suggested Citation

  • Fosgerau, Mogens & McFadden, Daniel & Bierlaire, Michel, 2010. "Choice probability generating functions," MPRA Paper 24214, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:24214
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    References listed on IDEAS

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    8. Bierlaire, M. & Bolduc, D. & McFadden, D., 2008. "The estimation of generalized extreme value models from choice-based samples," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 381-394, May.
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    11. McFadden, Daniel, 1974. "The measurement of urban travel demand," Journal of Public Economics, Elsevier, vol. 3(4), pages 303-328, November.
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    Citations

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    Cited by:

    1. Mogens Fosgerau & André de Palma, 2016. "Generalized entropy models," Working Papers hal-01291347, HAL.
    2. Mogens Fosgerau & Julien Monardo & André de Palma, 2019. "The Inverse Product Differentiation Logit Model," Working Papers hal-02183411, HAL.
    3. Nelson Lind & Natalia Ramondo, 2023. "Trade with Correlation," American Economic Review, American Economic Association, vol. 113(2), pages 317-353, February.
    4. Mogens Fosgerau & Emerson Melo & André de Palma & Matthew Shum, 2020. "Discrete Choice And Rational Inattention: A General Equivalence Result," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1569-1589, November.
    5. Mogens Fosgerau & Dennis Kristensen, 2021. "Identification of a class of index models: A topological approach," The Econometrics Journal, Royal Economic Society, vol. 24(1), pages 121-133.
    6. Fosgerau, Mogens & de Palma, André, 2015. "Demand systems for market shares," MPRA Paper 62106, University Library of Munich, Germany.
    7. Mattsson, Lars-Göran & Weibull, Jörgen W. & Lindberg, Per Olov, 2014. "Extreme values, invariance and choice probabilities," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 81-95.
    8. Daniel L. McFadden & Mogens Fosgerau, 2012. "A theory of the perturbed consumer with general budgets," NBER Working Papers 17953, National Bureau of Economic Research, Inc.
    9. Fosgerau, Mogens & Frejinger, Emma & Karlstrom, Anders, 2013. "A link based network route choice model with unrestricted choice set," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 70-80.
    10. Mogens Fosgerau, 2014. "Nonparametric approaches to describing heterogeneity," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 11, pages 257-267, Edward Elgar Publishing.
    11. Nelson Lind & Natalia Ramondo, 2023. "Global Innovation and Knowledge Diffusion," American Economic Review: Insights, American Economic Association, vol. 5(4), pages 494-510, December.
    12. Joao Macieira & Pedro Pereira & Joao Vareda, 2013. "Bundling Incentives in Markets with Product Complementarities: The Case of Triple-Play," Working Papers 13-15, NET Institute.
    13. Lurkin, Virginie & Garrow, Laurie A. & Higgins, Matthew J. & Newman, Jeffrey P. & Schyns, Michael, 2018. "Modeling competition among airline itineraries," Transportation Research Part A: Policy and Practice, Elsevier, vol. 113(C), pages 157-172.
    14. Stephane Hess & Andrew Daly & Richard Batley, 2018. "Revisiting consistency with random utility maximisation: theory and implications for practical work," Theory and Decision, Springer, vol. 84(2), pages 181-204, March.
    15. Tien Mai & Patrick Jaillet, 2019. "Robust Product-line Pricing under Generalized Extreme Value Models," Papers 1912.09552, arXiv.org, revised Oct 2021.
    16. Eliasson, Jonas & Fosgerau, Mogens, 2019. "Cost-benefit analysis of transport improvements in the presence of spillovers, matching and an income tax," Economics of Transportation, Elsevier, vol. 18(C), pages 1-9.
    17. Matthew Kovach & Gerelt Tserenjigmid, 2022. "Behavioral Foundations of Nested Stochastic Choice and Nested Logit," Journal of Political Economy, University of Chicago Press, vol. 130(9), pages 2411-2461.
    18. Kazagli, Evanthia & Bierlaire, Michel & Flötteröd, Gunnar, 2016. "Revisiting the route choice problem: A modeling framework based on mental representations," Journal of choice modelling, Elsevier, vol. 19(C), pages 1-23.
    19. Lai, Xinjun & Bierlaire, Michel, 2015. "Specification of the cross-nested logit model with sampling of alternatives for route choice models," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 220-234.
    20. Mogens Fosgerau & Abhishek Ranjan, 2017. "A note on identification in discrete choice models with partial observability," Theory and Decision, Springer, vol. 83(2), pages 283-292, August.
    21. Pereira, Pedro & Ribeiro, Tiago & Vareda, João, 2013. "Delineating markets for bundles with consumer level data: The case of triple-play," International Journal of Industrial Organization, Elsevier, vol. 31(6), pages 760-773.
    22. Sander Cranenburgh & Marco Kouwenhoven, 2021. "An artificial neural network based method to uncover the value-of-travel-time distribution," Transportation, Springer, vol. 48(5), pages 2545-2583, October.

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    More about this item

    Keywords

    Discrete choice; random utility; mixture models; duration models; logit; generalised extreme value; multivariate extreme value;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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